For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. Which of these, if any, will cover all the space needed for the roof? Explain your answer, drawing a picture if necessary.
. foot = 1/3 of a yard
To determine which board will cover all the space needed for the roof, we need to compare the sizes of the boards.
First, let's convert the measurements to a consistent unit. Since 1 yard is equal to 3 feet, we can convert the first board from square yards to square feet by multiplying by 9 (since 1 square yard = 3 feet * 3 feet = 9 square feet).
1 square yard = 1 * 9 = 9 square feet
So, the first board measures 9 square feet.
Next, let's convert the measurements for the second board from feet to square feet.
3 feet * 3 feet = 9 square feet
So, the second board also measures 9 square feet.
Finally, let's convert the measurements for the third board from inches to square feet.
36 inches * 36 inches = 1296 square inches
To convert square inches to square feet, we divide by 144 (since 1 square foot = 12 inches * 12 inches = 144 square inches).
1296 square inches / 144 = 9 square feet
So, the third board also measures 9 square feet.
Therefore, all three boards will cover the space needed for the roof since they all have the same area of 9 square feet.